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November  2010, 4(4): 571-577. doi: 10.3934/ipi.2010.4.571

Mathematical reminiscences

Jan Boman 1,

1. 

Department of Mathematics, Stockholm University, SE-10691 Stockholm, Sweden

Published  September 2010

N/A
Citation: Jan Boman. Mathematical reminiscences. Inverse Problems and Imaging, 2010, 4 (4) : 571-577. doi: 10.3934/ipi.2010.4.571
References:
[1]

J. Boman, On the propagation of analyticity of solutions of differential equations with constant coefficients, Ark. Mat., 5 (1964), 271-279. doi: doi:10.1007/BF02591127.

[2]

J. Boman, On the intersection of classes of infinitely differentiable functions, Ark. Mat., 5 (1964), 301-309. doi: doi:10.1007/BF02591130.

[3]

J. Boman, Partial regularity of mappings between Euclidean spaces, Acta Math., 119 (1967), 1-25. doi: doi:10.1007/BF02392077.

[4]

J. Boman, Differentiability of a function and of its compositions with functions of one variable, Math. Scand., 20 (1967), 249-268.

[5]

J. Boman, (joint work with H. S. Shapiro), Comparison theorems for a generalized modulus of continuity, Bull. Amer. Math. Soc., 75 (1969), 1266-1268. doi: doi:10.1090/S0002-9904-1969-12387-6.

[6]

J. Boman, (joint work with H. S. Shapiro), Comparison theorems for a generalized modulus of continuity, Ark. Mat., 9 (1971), 91-116. doi: doi:10.1007/BF02383639.

[7]

J. Boman, Saturation problems and distribution theory, Appendix I in "Topics in Approximation Theory," by H. S. Shapiro, Lecture Notes in Mathematics, no. 187 (1971), pp. 249-266.

[8]

J. Boman, Equivalence of generalized moduli of continuity, Ark. Mat., 18 (1980), 73-100. doi: doi:10.1007/BF02384682.

[9]

J. Boman, On the closure of spaces of sums of ridge functions and the range of the X-ray transform, Ann. Inst. Fourier (Grenoble), 34 (1984), 207-239.

[10]

J. Boman, An example of non-uniqueness for a generalized Radon transform, J. d'Anal. Math., 61 (1993), 395-401. doi: doi:10.1007/BF02788850.

[11]

J. Boman, (joint work with E. T. Quinto) Support theorems for real-analytic Radon transforms, Duke Math. J., 55 (1987), 943-948. doi: doi:10.1215/S0012-7094-87-05547-5.

[12]

J. Boman, The sum of two plane convex $C^{\infty}$ sets is not always $C^5$, Math. Scand., 66 (1990), 216-224.

[13]

J. Boman, Smoothness of sums of convex sets with real analytic boundaries, Math. Scand., 66 (1990), 225-230.

[14]

J. Boman, (joint work with E. T. Quinto), Support theorems for real-analytic Radon transforms on line complexes in three-space, Trans. Amer. Math. Soc., 335 (1993), 877-890. doi: doi:10.2307/2154410.

[15]

J. Boman, Helgason's support theorem for Radon transforms - a new proof and a generalization, Lecture Notes in Mathematics no. 1497 (1989), 1-5.

[16]

J. Boman, A local vanishing theorem for distributions, C. R. Acad. Sci. Paris, 315 Série I (1992), 1231-1234.

[17]

J. Boman, Holmgren's uniqueness theorem and support theorems for real analytic Radon transforms, Contemp. Math., 140 (1992), 23-30.

[18]

J. Boman, Microlocal quasianalyticity for distributions and ultradistributions, Publ. RIMS (Kyoto), 31 (1995), 1079-1095. doi: (MR1382568) doi:10.2977/prims/1195163598.

[19]

J. Boman, (joint work with Svante Linusson), Examples of non-uniqueness for the combinatorial Radon transform modulo the symmetric group, Math. Scand., 78 (1996), 207-212.

[20]

J. Boman, Uniqueness and non-uniqueness for microanalytic continuation of hyperfunctions, Contemp. Math., 251 (2000), 61-82.

[21]

J. Boman, (joint work with Lars Hörmander), A Payley-Wiener theorem for the analytic wave front set, Asian J. Math., 3 (1999), 757-769.

[22]

J. Boman, (joint work with Jan-Olov Strömberg), Novikov's inversion formula for the attenuated Radon transform-A new approach, J. Geom. Anal., 14 (2004), 185-198.

[23]

J. Boman, (joint work with Filip Lindskog), Support theorems for the Radon transform and Cramér-Wold theorems, J. Theor. Probab., 22 (2008), 683-710. doi: doi:10.1007/s10959-008-0151-0.

[24]

J. Boman, The mathematics of tomography. On a mathematical theory with many new applications (Swedish), Normat, 56 (2008), 177-186.

[25]

J. Boman, Unique continuation of microlocally analytic distributions and injectivity theorems for the ray transform, Inverse Probl. Imaging, in this issue.

[26]

J. Boman, (joint work with Dieudonné Agbor), On the modulus of continuity of mappings between Euclidean spaces, to appear in Math. Scand.

[27]

J. Boman, A local uniqueness theorem for a weighted Radon transform, Inverse Probl. Imaging, in this issue.

[28]

J. Boman, Flatness of distributions vanishing on infinitely many hyperplanes, C. R. Acad. Sci. Paris, Série I, 347 (2009), 1351-1354.

[29]

L. Hörmander, "The Analysis of Linear Partial Differential Operators,'' Vol. 1, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1983.

[30]

R. G. Novikov, An inversion formula for the attenuated X-ray transform, Ark. Mat., 40 (2002), 145-167. doi: doi:10.1007/BF02384507.

[31]

S. Gindikin, A Remark on the weighted Radon transform on the plane, J. Inverse Probl. Imaging, in this issue.

[32]

H. S. Shapiro, A Tauberian theorem related to approximation theory, Acta Math., 120 (1968), 279-292. doi: doi:10.1007/BF02394612.

show all references

References:
[1]

J. Boman, On the propagation of analyticity of solutions of differential equations with constant coefficients, Ark. Mat., 5 (1964), 271-279. doi: doi:10.1007/BF02591127.

[2]

J. Boman, On the intersection of classes of infinitely differentiable functions, Ark. Mat., 5 (1964), 301-309. doi: doi:10.1007/BF02591130.

[3]

J. Boman, Partial regularity of mappings between Euclidean spaces, Acta Math., 119 (1967), 1-25. doi: doi:10.1007/BF02392077.

[4]

J. Boman, Differentiability of a function and of its compositions with functions of one variable, Math. Scand., 20 (1967), 249-268.

[5]

J. Boman, (joint work with H. S. Shapiro), Comparison theorems for a generalized modulus of continuity, Bull. Amer. Math. Soc., 75 (1969), 1266-1268. doi: doi:10.1090/S0002-9904-1969-12387-6.

[6]

J. Boman, (joint work with H. S. Shapiro), Comparison theorems for a generalized modulus of continuity, Ark. Mat., 9 (1971), 91-116. doi: doi:10.1007/BF02383639.

[7]

J. Boman, Saturation problems and distribution theory, Appendix I in "Topics in Approximation Theory," by H. S. Shapiro, Lecture Notes in Mathematics, no. 187 (1971), pp. 249-266.

[8]

J. Boman, Equivalence of generalized moduli of continuity, Ark. Mat., 18 (1980), 73-100. doi: doi:10.1007/BF02384682.

[9]

J. Boman, On the closure of spaces of sums of ridge functions and the range of the X-ray transform, Ann. Inst. Fourier (Grenoble), 34 (1984), 207-239.

[10]

J. Boman, An example of non-uniqueness for a generalized Radon transform, J. d'Anal. Math., 61 (1993), 395-401. doi: doi:10.1007/BF02788850.

[11]

J. Boman, (joint work with E. T. Quinto) Support theorems for real-analytic Radon transforms, Duke Math. J., 55 (1987), 943-948. doi: doi:10.1215/S0012-7094-87-05547-5.

[12]

J. Boman, The sum of two plane convex $C^{\infty}$ sets is not always $C^5$, Math. Scand., 66 (1990), 216-224.

[13]

J. Boman, Smoothness of sums of convex sets with real analytic boundaries, Math. Scand., 66 (1990), 225-230.

[14]

J. Boman, (joint work with E. T. Quinto), Support theorems for real-analytic Radon transforms on line complexes in three-space, Trans. Amer. Math. Soc., 335 (1993), 877-890. doi: doi:10.2307/2154410.

[15]

J. Boman, Helgason's support theorem for Radon transforms - a new proof and a generalization, Lecture Notes in Mathematics no. 1497 (1989), 1-5.

[16]

J. Boman, A local vanishing theorem for distributions, C. R. Acad. Sci. Paris, 315 Série I (1992), 1231-1234.

[17]

J. Boman, Holmgren's uniqueness theorem and support theorems for real analytic Radon transforms, Contemp. Math., 140 (1992), 23-30.

[18]

J. Boman, Microlocal quasianalyticity for distributions and ultradistributions, Publ. RIMS (Kyoto), 31 (1995), 1079-1095. doi: (MR1382568) doi:10.2977/prims/1195163598.

[19]

J. Boman, (joint work with Svante Linusson), Examples of non-uniqueness for the combinatorial Radon transform modulo the symmetric group, Math. Scand., 78 (1996), 207-212.

[20]

J. Boman, Uniqueness and non-uniqueness for microanalytic continuation of hyperfunctions, Contemp. Math., 251 (2000), 61-82.

[21]

J. Boman, (joint work with Lars Hörmander), A Payley-Wiener theorem for the analytic wave front set, Asian J. Math., 3 (1999), 757-769.

[22]

J. Boman, (joint work with Jan-Olov Strömberg), Novikov's inversion formula for the attenuated Radon transform-A new approach, J. Geom. Anal., 14 (2004), 185-198.

[23]

J. Boman, (joint work with Filip Lindskog), Support theorems for the Radon transform and Cramér-Wold theorems, J. Theor. Probab., 22 (2008), 683-710. doi: doi:10.1007/s10959-008-0151-0.

[24]

J. Boman, The mathematics of tomography. On a mathematical theory with many new applications (Swedish), Normat, 56 (2008), 177-186.

[25]

J. Boman, Unique continuation of microlocally analytic distributions and injectivity theorems for the ray transform, Inverse Probl. Imaging, in this issue.

[26]

J. Boman, (joint work with Dieudonné Agbor), On the modulus of continuity of mappings between Euclidean spaces, to appear in Math. Scand.

[27]

J. Boman, A local uniqueness theorem for a weighted Radon transform, Inverse Probl. Imaging, in this issue.

[28]

J. Boman, Flatness of distributions vanishing on infinitely many hyperplanes, C. R. Acad. Sci. Paris, Série I, 347 (2009), 1351-1354.

[29]

L. Hörmander, "The Analysis of Linear Partial Differential Operators,'' Vol. 1, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1983.

[30]

R. G. Novikov, An inversion formula for the attenuated X-ray transform, Ark. Mat., 40 (2002), 145-167. doi: doi:10.1007/BF02384507.

[31]

S. Gindikin, A Remark on the weighted Radon transform on the plane, J. Inverse Probl. Imaging, in this issue.

[32]

H. S. Shapiro, A Tauberian theorem related to approximation theory, Acta Math., 120 (1968), 279-292. doi: doi:10.1007/BF02394612.

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